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On the IBM Quantum Composer website, there are characteristics of qubit computers. For example, ibmq_16_melbourne. But there is no description anywhere of what:

T1(us), T2(us), Frequency (GHz), Readout assignment error, Prob meas0 prep1, Prob meas1 prep0, Readout length (ns), ID error, √x (sx) error, Single-qubit Pauli-X error, CNOT error, Gate time (ns) means.

Could you write down what they mean?

And why isn't there, for example, a Pauli-Z error, even though there is a Pauli-X error?

Characteristics of the IBM quantum computer

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    $\begingroup$ To close voters: It has a fabulous answer, so please stop. $\endgroup$ Commented Apr 15, 2021 at 17:51

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A quick and dirty list:

  • $T_{1}$ and $T_{2}$ - colloquially known as decoherence times, but slightly more precisely also as the (qubit) relaxation time ($T_{1}$) and the (qubit) dephasing time ($T_{2}$).
  • $T_{1}$ is a measure of how quickly a qubit in the excited ($|1\rangle$) state spontaneously relaxes to the ground ($|0\rangle$) state.
  • $T_{2}$ is slightly more tricky: it is a measure of how fast a coherent superposition (one with a well-defined relative phase between the $|0\rangle$ and $|1\rangle$) loses this 'well-defined-ness'. Essentially, it's what makes a qubit a quantum phenomenon; a (completely) dephased qubit is just a probabilistic classical bit.
  • Frequency - the qubits from IBM are superconducting qubits. Interactions with these qubits are performed via microwave resonators; to address each different qubit separately each' qubits resonator has a different frequency. As @Lena has pointed out, the frequency is actually defined as the energy difference between the $|0\rangle$ and $|1\rangle$ states.
  • Readout assignment error - measure of how well the measurement performs - as luciano mentions in his answer, the probability of a measurement returning the wrong value.
  • Prob meas0 prep1 - The probability that a measurement returns $0$ immediately after preparing the $|1\rangle$ state. A combination of faulty preparation and faulty measurements; these are also often referred to as SPAM (state-preparation-and-measurement) errors.
  • Prob meas1 prep0 - like the previous one
  • Readout length (ns) - time it takes to perform a measurement in (ns). One of the main limiting factors of current quantum hardware; as these times are often considerably longer than the $T_{2}$, which makes intermediate measurements (i.e. measurements that are not at the end of a circuit) practically unfeasible.
  • ID error - measure of the error induced by having the qubit idle (for a typical gate time). The measure used is, I believe, that 'returned' by randomized benchmarking, which closely resembles the process fidelity.
  • $\sqrt{X}$ error - measure of error induced by applying the gate in question. Average over all different qubits.
  • Single-qubit Pauli X error - likewise
  • CNOT error - error of the only two-qubit gate natively implementable on the IBM devices. Average over all possible CNOT gates
  • Gate time (ns) - Lena to the rescue again - this is related to the time it takes to perform a CNOT, the two-qubit gate.

And why isn't there, for example, a Pauli-Z error, even though there is a Pauli-X error?

The reason there is no error shown for the Pauli Z is because there is (virtually) none. This is because the IBM machines don't really implement $Z$ rotations - they keep track of the $Z$ rotations through software, and update the $X$ (and $Y$) gates accordingly. Effectively, they rotate the $X$ and $Y$ axes of the Bloch sphere along the $Z$ axis - the 'Pauli X' gate is thus actually any rotation along an axis in the $X-Y$ plane of the Bloch sphere. By changing the phase of the induced wave on the resonator, one can pick the angle the axis makes with a predetermined reference point, and thus implement both $X$ and $Y$ gates.

You might also find this page on system properties and this qiskit notebook on calibration useful.

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  • $\begingroup$ Regarding square root X error what's the meaning of the sentence "Average over all different qubits." Does this mean that the error is divided by the number of qubits in the ibmq system ? or you mean they test the system many times and calculate the average error for each qubit ? or something else ? Please clarify the meaning for me. $\endgroup$ Commented May 24, 2021 at 23:54
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Just adding some stuff to the already good answer :

  • The gate time actually is related to the connexion between qubits, so is related to the CNOT, not the single-qubit gates.
  • The frequency is defined as the difference in energy between the ground and excited states, i.e. the |0⟩ and |1⟩ states, respectively.
  • for more info about how to measure all this (T1, T2, frequency), you could check this tutorial showing all this.
  • about the errors of Z/X, the basis gates of all the different available backends are the cx, x, sx, and rz. So you won't have any error rate for Z but you will have for X because of this.
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  • $\begingroup$ Thanks, do you mind if I merge this with my current answer? $\endgroup$ Commented Apr 15, 2021 at 9:43

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